Changes between Version 13 and Version 14 of u/EricasLibrary

Timestamp:

09/13/11 12:15:52 (13 years ago)

Author:

Erica Kaminski

Comment:

—

u/EricasLibrary

@@ -35 +35 @@
 [[CollapsibleStart(Foster and Chevalier (‘93))]]
 
+=== Motivation === 
+
+While the collapse problem of an isothermal sphere is well studied, there remains some conflict on the correct analytic solution for the collapse. Larson and Penston (1969) produced a solution for the collapse problem that was later criticized by Shu (1977) as being ad hoc in some of the mathematical formulations. Later numerical studies by Hunter (1977), however, showed that the collapse does follow the LP solution. Despite this, the Shu solution remains the prominent treatment of the problem. The authors here set out to check which solution indeed describes the collapse problem. 
+
 === Summary === 
 
-Authors ran simulations with an outer density of 1/1000 the density at the outermost edge of the clump, whereas my simulations used 1/100. The ambient therefore had a large sound speed throughout the constant pressure medium (pressure = pressure in sphere at edge), and since the ambient region was very large, the pressure remained nearly constant throughout. They found that if the sphere was initialized with the Larson-Penston solution, it followed the analytical LP soln'. If grid was initialized to by the singular isothermal sphere, it followed Shu's solution. 
+Authors ran simulations with an outer density of 1/1000 the density at the outermost edge of the clump, whereas my simulations used 1/100. The ambient therefore had a large sound speed throughout the constant pressure medium (pressure = pressure in sphere at edge), and since the ambient region was very large, the pressure remained nearly constant throughout. They found that if the sphere was initialized with the Larson-Penston solution, it followed the analytical LP soln'. If the grid was initialized by a singular isothermal sphere, it followed Shu's solution. 
 
 === Stability Tests === 
@@ -46 +50 @@
 * xi = 6.451, collapse happened in 5 ff times
 * xi = 20, collapse happened in 6 ff times
+
+=== Collapse Results === 
+
+- Inflow is initially marked by velocity proportional to r for small r, peaking at xi = 2, and turning back to 0 velocity out toward edge of sphere.
+
+- Simulation approaches LP solution in center region.
+
+- Velocity becomes constant in inner region after core formation, ~ 3Cs
+
+- Inner region evolves fast, outer evolves slow.
+
+- Core formation is not a subsonic adjustment of density with radius as Shu said. The inner regions collapse to a core supersonically.
+
+- Should compare anything to mass accretion rate?